Clicker Question 1

What is x sin(3x) dx ?– A. (1/3)cos(3x) + C– B. (-1/3)x cos(3x) + (1/9)sin(3x) + C– C. -x cos(3x) + sin(3x) + C– D. -3x cos(3x) + 9sin(3x) + C– E. (1/3)x cos(3x) - (1/9)sin(3x) + C

Clicker Question 2

What is ?

– A. e – 1– B. ¼(e2 – 1)– C. ¼(e2 + 1)– D. 4(e2 + 1)– E. e + 1

e

dxxx1

)ln(

Trig Integrals (2/7/14)

Trig integrals can often be done by recalling the basic trig derivatives and using some basic trig identities:

sin2(x) + cos2(x) = 1 1 + tan2(x) = sec2(x) (“Pythagorean Identities”) cos(2x) = cos2(x) – sin2(x) (“Double angles”)

= 2cos2(x) – 1 = 1 – 2sin2(x)

Three Examples

sin2(x) cos3(x) dx ??

tan(x) sec4(x) dx ??

sin2(x) dx

Clicker Question 3

What is sin3(x) dx ?– A. cos(x) – (1/3)cos3(x) + C– B. (1/3)cos3(x) – cos(x) + C– C. x – (1/3)cos3(x) + C– D. (1/3)cos3(x) – x + C– E. (1/4)sin4(x) + C

Another Non-Obvious Trig Antiderivative Fact

Recall that tan(x) dx = -ln(cos(x)) + C

= ln(sec(x)) + C

What is sec(x) dx ??

(Hint: Multiply top and bottom bysec(x) + tan(x))

Assignment for Monday

Read Section 7.2. Do Exercises 3, 7, 13 (Hint: We worked out

in class what an antiderivative of sin2(t) is), 23, 55, 61.